What Is A Polygon? Definition, Types, And Properties Of Polygon

A quadrilateral is a two-dimensional shape with 4 sides. Here you will find examples of various quadrilateral 4-sided shapes as well as definitions, types, examples, and all special properties of quadrilaterals. Let’s get started now!

Have you ever heard of a polygon? What images do you have in mind when you think of a polygon? The tiles on which you walk are most likely square or hexagonal, indicating that it is polygonal. A polygon can be found in real-life objects such as a stop sign on the side of the road, a table, or a ball. This article will explain the meaning and definition of a polygon, the different types of polygons, as well as their characteristics, and relevant formulas.

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What is a Polygon? 

Polygons are two-dimensional geometric figures with a fixed number of sides. A polygon’s sides are made up of straight line segments that are connected end to end. As a result, the line segments of a polygon are referred to as sides or edges. The point where 2 line segments cross is known as the vertex or corner, and an angle is formed as a result. A triangle with 3 sides is an example of a polygon. A circle is a plane figure, but it isn’t considered a polygon since it is curved and lacks sides and angles. As a result, we can say that all polygons are 2d shapes, but not all 2d figures are polygons.

Polygon Chart

This table indicates the naming convention for polygons determined by the number of sides. Each polygon is given a unique name based on the number of sides, thus when the polygon’s name is written, its one part is also affected by the number of sides. The trigon, also known as the triangle, is made up of two words: “tri” which means 3 and gon which implies angles, indicating that it is a shape with three angles.

Types of Polygons

We understand what a polygon is. Is there anything else to it? Yes! There is, of course! Polygons are divided into various types based on the number of sides and the extent of the angles.

Regular polygons, irregular polygons, convex polygons, concave polygons, quadrilateral polygons, pentagon polygons, and so on are some of the most common types of polygons. Triangles, squares, parallelograms, rectangles, pentagons, rhombuses, hexagons, and other well-known polygons

Regular polygon

Considering a regular polygon, all sides of this polygon are equal. Moreover, all of the interior angles are equal as well.

Irregular polygon

These are irregularly shaped polygons. Nothing is equal when compared to a regular polygon, whether the sides or the angles.

Concave polygon

A concave polygon is one with at least one angle greater than 180 degrees. A concave polygon’s vertices are also inwards and outwards.

Convex polygon

The interior angle of a convex polygon is always less than 180 degrees. This type of polygon is the inverse of a concave polygon. Furthermore, the vertices of a convex polygon always point outwards.

Quadrilateral polygon

Four-sided polygons, also known as quadrilateral polygons, are quite common. A quadrilateral polygon can be divided into several types: Trapezium, Kite, Parallelogram, Rectangle, Rhombus, and Square

Pentagon polygon

Pentagon polygons have six sides. It is crucial to note that the length of the polygon’s five sides remains constant. A regular pentagon is the most common type of pentagon polygon.

Angles in a Regular Polygon

There are two types of angles in the case of a regular polygon. They include:

• Interior Angles of a Polygon
• Exterior Angles of a Polygon

Interior Angles of a Polygon

In the case of a regular polygon, the interior angles are created between the adjacent sides inside the polygon and are the same as each other. The total number of interior angles equals the total number of sides. The value of an interior angle of a regular polygon could be determined with the following formula if the number of sides of the regular polygon is known:

Interior angle = 180º(n-2)/n, where n represents the number of sides

Exterior Angles of a Polygon

So every exterior angle of a regular polygon is created by extending one of its sides (clockwise or anticlockwise) and measuring the angle between that extension and the adjacent side. Each exterior angle of a regular polygon is similar, and the sum of the polygon’s exterior angles is 360°. If the number of sides in a regular polygon is identified, the exterior angle could be determined using the following equation:

Exterior Angle = 360º/n, where n represents the number of sides

You should note that:

• Polygons are two-dimensional figures with more than three sides.
• The following formulas can be used to calculate the angles of a regular polygon:
  Exterior Angle = 360º/n
  Interior angle = 180º(n-2)/n, where n is the number of sides.
• Because they form a linear pair of angles, the total value of interior and exterior angles at a point is always 180º
• The number of diagonals in an ‘n’-sided polygon can be determined using this formula: n(n-3)/2.

Polygon Formulas

Polygons have two basic formulas, which are listed below:

• Area of polygons
• Perimeter of polygons

Let’s take a closer look at the two polygon formulas mentioned above.

Area of Polygons

The area of a polygon is the calculation of the space enclosed by a polygon. Based on whether the polygon is regular or irregular, separate formulas can be used to calculate its area. A triangle, for example, is a three-sided polygon known as a trigon. The method for determining the area of a trigon (triangle) is half the product of the triangle’s base and height. It is measured in m², cm², and ft².

Perimeter of Polygons

The perimeter of a polygon is the distance around a polygon that can be calculated by adding the lengths of all given sides.

Polygon perimeter formula = length of side 1 + length of side 2 + length of side 3…+ length of side N (for an N-sided polygon). It is defined in terms of units such as meters, centimeters, feet, and so on.

When do kids start learning about polygons?

Polygons are an important part of the math curriculum. This means that they will be taught to kids throughout their primary school years. However, here is a rough outline of what students can expect from polygon teaching at each level:

• Year 1 – Children will learn the names of common 2D shapes like squares, triangles, pentagons,  rectangles, hexagons, and octagons. Flashcards, matching games, printable worksheets, and looking for examples of these shapes in real-world situations can help kids understand this.
• Year 2 – Students will be taught to recognize shape properties like the number of sides and vertices (corners). They will count the total number of sides and vertices on the shape. They will identify shapes using properties such as This shape has three sides and three corners. What is it?
• Year 3 – Children will broaden their understanding of polygons to include various types of triangles and quadrilaterals. They will learn about heptagons, nonagons, and decagons. Angles and symmetry of these polygons will be included in their knowledge of shape properties. Kids will explain and identify shapes based on their properties such as symmetry and angles. They may be asked to use Venn diagrams and Carroll diagrams to classify shapes based on their properties.
• Year 4 – Students learn to compare the lengths and angles of polygons to determine whether they are regular or irregular. The terms “polygon,” “regular,” and “irregular” will be utilized. Kids will be given a variety of polygons to classify into regular and irregular; this could be done through practical tasks or through the use of ICT.
• Year 5 – Using reasoning about equal sides and angles, kids will be taught to distinguish between regular and irregular polygons. They will be given shapes to classify and will be required to describe why the polygon is regular using angle and side properties.
• Year 6 – Students start to discover unknown angles in regular polygons at the end of KS2. They will be shown how to use their understanding of angles and a given formula to determine unknown angles in polygons.

Hope that with the above information about Polygon shape, you can get a clear lesson plan to help your children easily grasp the answer to the question “what is a polygon”. If you are planning to teach your kids about this essential topic, you can make your own collections of Polygon worksheets using our worksheet maker.